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C₂×#26366 #6439165

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

(1,2);(3,4)(5,6)(7,8,11,13)(9,12,10,14)(16,19)(20,22);(4,6)(7,9,11,10)(8,12,13,14)(16,20)(18,21)(19,22);(7,10,11,9)(8,12,13,14)(15,16)(17,19)(18,22)(20,21);(4,6)(16,19)(20,22)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6346361);